Eugeniusz Rusiński
Professor
Wroclaw University of Technology
Faculty of Mechanical Engineering, Poland
Jerzy Czmochowski
Associated Professor
Wroclaw University of Technology
Faculty of Mechanical Engineering, Poland
Przemysław Moczko
Assistant Professor
Wroclaw University of Technology
Faculty of Mechanical Engineering, Poland
Damian Pietrusiak
Assistant Professor
Wroclaw University of Technology
Faculty of Mechanical Engineering, Poland
Assessment of the Correlation
Between the Numerical and
Experimental Dynamic Characteristics
of the Bucket Wheel Excavator in
Terms of the Operational Conditions
In the paper authors present their attempt in the validation process of the
numerical model on the basis of experimental results. The Modal
Assurance Criterion between the numerical and experimental model was
selected as the indicating factor. Moreover, changes in frequencies and the
degrees of freedom influencing the most the correlation level were
reconsidered.
The numerical and experimental models, in most cases, did not cover the
influence of the operational load on the dynamic characteristic of the
construction. In the new, operational approach, the change in the
numerical model composition must be reconsidered, while the old one is no
longer valid. Modal analysis performed out of the operational load, give
good results but does not represent actual state of the construction in
operation. In that case, we have two separate systems with different
dynamic characteristics. Identification of the modal model with use of the
Operational Modal Analysis gives the information about the object in
operation which is a real point of the interest.
Keywords: Modal Analysis, Bucket Wheel Excavator.
1.
INTRODUCTION
At present, most of the surface mining machines
working in the lignite mines in Poland are even twenty
or thirty years old. In the case of such complicated
structures, proper and sufficient identification of
dynamic characteristics was not fully achievable till
now. Recent development of mathematical, numerical
methods and the power of computers allowed to face
with that problem in full scale [1]. Up to now the only
reliable method for determination of dynamic
characteristics was an experiment. Obtained results gave
full information but about the already built object. What
is more, proper implementation of the experimental
procedure on such objects is not a simple task [2-4].
Dynamic characteristic of the object is a useful
needle for the operation of the machine [5], especially in
the case of the big size surface mining machines which
are highly exposed to the dynamic load. This type of
machines are spreaders (Figure 1) and bucket wheel
excavators (Figure 2) [6].
In the case of excavators, the high variability of the
excavation force is a common phenomenon [7].
Additionally, vibrations are generated in drives [8],
conveyors [9] and by the transported material (hitting
the pulleys and discharge points). Technological
movements like travel, rotation or derricking are also a
source of vibrations. Spreaders are not so exposed to the
Received: September 2013, Accepted: November 2013
Correspondence to:Dr Damian Pietrusiak
Faculty of Mechanical Engineering,
Wroclaw University of Technology
Lukasiewicza 7/9, 50-371 Wroclaw, Poland
E-mail: [email protected]
© Faculty of Mechanical Engineering, Belgrade. All rights reserved
dynamical loads as bucket wheel excavators, but due to
their slenderness it is also easier to excite vibrations.
In reduction of negative results of the vibrations,
knowledge about dynamical characteristics is one of the
key factors. An indirect result of the amplitude decrease
is the significant positive influence on durability of the
structure, mainly due to the fatigue phenomenon
reduction [10]. There are known cases where dynamical
displacements lead to the collision of the machine
elements [11]. Proper identification of the modal model
allowed to implement changes in construction that will
prevent this negative phenomenon. Nowadays, even
more sophisticated methods [12-14] can be applied to
reduce the vibration but still good identification of a
modal model is needed. In many other cases, operation
in resonant areas makes the operation difficult.
What is worth noting, the vibrations generated by
the machines can also excite human organs vibrations.
Permissible acceleration levels are defined in the
standards [15-16]. In ultimate cases, human body organs
can vibrate in resonance. Following the general trends
of human protection [17-19], vibrations must also be
taken into consideration.
2. OBJECT OF INVESTIGATIONS
Preliminary investigations performed on the bucket
wheel excavator SchRs 4600.50 [20] revealed that the
correlation level of numerical and experimental results
differ in particular operational conditions. This lead to
the conclusion that an attempt to update numerical
models should be done to obtain better correlation.
FME Transactions (2013) 41, 298-304 298
Figure 1. Spreader A2RSB12500
Also, the source of differences between
experimental models should be investigated. Both of the
problems are discussed in the present paper.
The investigated object was the bucket wheel
excavator SchRs 4600.50 (Figure 1). This is one of the
biggest surface mining machines operating in Poland.
The height exceeds 64 me-ters, length 120 meters and
the mass (without discharge bridge) is around 5000
tonns.
Figure 2. Bucket wheel excavator SchRs 4600.50
The necessity for investigations of the dynamic
behavior was caused by the need of modernization of
the excavating unit [21]. Excitation generated during
machine operation is the key factor influencing the
vibrations of the machine. Detailed information about
the dynamic characteristics of the object allowed to
design a new bucket wheel with properly selected
number of buckets (direct influence on the excitation
frequency).
3. NUMERICAL MODAL ANALYSIS
A Discrete model of the complete superstructure of the
machine consists of the slewing platform, counterweight
FME Transactions
boom, central part, bucket wheel boom and front and
rear tower. In the numerical model, undercarriage
elements like platform or driving elements assemblies
and the discharge bridge were not included. Those
elements were taken under consideration, while the
most important, concerning vibrations problem is the
superstructure. However, stiffness of the undercarriage
elements must be substituted in the model in other way,
while it influences the global modes of the machine. In
the described discrete model the bucket wheel excavator
SchRs 4600.50 superstructure was supported in the area
where railway of the main bearing is assembled. The
stiffness of the reduction elements was adjusted to the
stiffness of all the undercarriage parts. This approach
gives only approximated representation of the real
conditions. But, even if the whole undercarriage were
included to the simulations there is still big unknown of
the ground stiffness and even perfectly built model of
the whole machine does not give the exact stiffness
value. Eventually, results point out that the simplified
approach allows to obtain results on the satisfied level.
Results of the performed numerical simulations are
presented in the Table 1. Eight main modes were
selected and most of them are the global one.
4. ON SITE MEASUREMENTS AND RELATION WITH
NUMERICAL RESULTS
Numerical measurements gave the basis for the
preparation of proper modal experiment in real
conditions. At first, the measurement points were
selected (Figure 3).
Measurements were taken in several operational
conditions, which can be observed during lifetime of the
excavator. From all the data sets, the three of them
(most reliable) were selected for the analysis: upward
excavation, downward excavation and machine travel.
Comparison of MAC [22] factor for each load case is
presented in Figure 3.
VOL. 41, No 4, 2013 ▪ 299
Mode
Description
Mode
Description
Mode 1–0.28Hz
bucket wheel
boom torsion
Mode 5-0.53Hz
bucket wheel and
counterweight
boom bending in
horizontal plane
Mode 2-0.32Hz
superstructure
vibrations
in vertical plane
Mode 6-0.82Hz side
vibrations of front and
rear mast
Mode 3-0.37Hz
superstructure
vibrations
in vertical plane
Mode 7-0.96
rear mast
bending
Mode 4-0.38Hz
superstructure
vibrations
in horizontal plane
Mode 8-1.68Hz front
mast
torsion
Table 1. Heading (Helvetica 8 bold) – Align left

f  fb
ku  fb   MACab  1  a

fb

Figure 3. Measurement points [18]
While independently of the load case the correlation
with numerical model did not change significantly [1],
the attempt for increasing the correlation of the
numerical and experimental modal model were
performed.
When comparing both modes, not only information
about the mode shape similarity, but also information
how it is related the frequency of compared mode is
important.
For that reason, to make it quick and easy, the
author’s generalized correlation factor (ku) was used in
the following form (1):
300 ▪ VOL. 41, No 4, 2013



(1)
where fa is the frequency of the mode from the
numerical model, fb is the frequency of the mode form
the experimental model MACab is the correlation of
numerical (a) and experimental (b) mode.
The modifications of the numerical model covered
boundary conditions related to the changes in
operational conditions. As main factors influencing
dynamics of the machine, circumferential force and
damping were assumed (Figure 5). This assumption was
made on the basis of the analysis of the experimental
results (Figure 4). It is visible that the operational
conditions influence most the global modes in the
vertical plane along the axis of the machine.
The damping coefficient value (ckr) was selected
according to the Eq. (2) [23]:

f  fb
ku  fb   MACab  1  a

fb




(2)
which describes the critical damping for the single
degree of freedom system. In the case of the global
vibration modes along the main axis of the machine in
the vertical plane, this assumption represents the
vibrations motion in a proper way.
FME Transactions
Figure 4. crossMAC factor for particular operational case
As a result, diagrams (Figure 6 to Figure 8) of the
generalized correlation factor between numerical model
(covering all the eleven load cases) and the particular
experimental case were prepared. It is visible that none
of the changes did influence significantly on the
correlation level, no matter what is the experimental
case. However, those simulations revealed that the
simplest model, based on the Stability Proof, is actually
FME Transactions
the most proper.This indicates additionally that for the
proper simulation of the changing operational condition,
more complex approach is required. With high
probability, the phenomenon of the interaction of the
buckets and excavated soil must be included.
Realization of that task required complicated
experimental studies that will give the basis for further
analysis.
VOL. 41, No 4, 2013 ▪ 301
Table 2. Numerical model boundary conditions.
Numerical model boundary conditions
Overburden and pollution of the
circumferential
superstructure
force
Lp.
superstructure according to the
Stability Proof
1
X
---
---
2
X
x
---
---
3
X
x
x
---
4
X
x
---
0,40
5
X
x
x
0,40
6
X
x
---
0,57
7
X
x
x
0,57
8
x
x
---
0,78
frequency value [Hz]
---
9
x
x
x
0,78
10
x
x
---
0,97
11
x
x
x
0,97
0,9
downward excavation
0,8
ku[‐]
0,7
0,6
0,5
0,4
0,3
0,2
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
1,8
fn[Hz]
Figure 8. Generalized correlation factor level for upward
excavation and numerical model (for every set from table 2)
Figure 5. Numerical model boundary conditions scheme
travel
0,9
0,8
ku[‐]
0,7
0,6
0,5
0,4
Additionally, if we analyze the response of the machine
in case of the operational condition, it is possible to see
that there is a difference in the band of the excitation.
This proves the relation between the operational
condition and the presence of the modal modes. If take a
look at the Figure 9 it is visible that the excitation
during excavation does not supply enough energy in the
lowest range of frequencies. On the other hand, the
travel is the case that can excite the modes even in the
lowest band. Even if there are no the characteristics of
excitation it is possible to describe it in general.
0,3
0
0,2
0,4
0,6
0,8
f[Hz]
1
1,2
1,4
1,6
1,8
Figure 6. Generalized correlation factor level for travel and
numerical model (for every set from table 2)
0,7
upward excavation
0,65
0,6
Figure 9. Excitation band for the excavation and travel case
ku[‐]
0,55
0,5
5. CONCLUSIONS
0,45
0,4
0,35
0,3
0
0,2
0,4
0,6
0,8
fn[Hz]
1
1,2
1,4
1,6
Figure 7. Generalized correlation factor level for upward
excavation and numerical model (for every set from table 2)
302 ▪ VOL. 41, No 4, 2013
In presented paper differences between particular
experimental modal models were presented. The level
of the correlation (crossMAC matrices) indicates the
presence of every particular mode in terms of
operational conditions.
FME Transactions
Moreover, the application of the generalized
correlation factor shows a simple and very useful
method for the comparison of correlation level, both
modal deflection shape and frequency. It was applied
for the comparison of the modified numerical model and
particular experimental modal model which correspond
to the particular operational case. No significant
changes in the correlation level were observable. This
leads to the conclusion that the simplest model, without
additional boundary conditions, gives the same results
like the modified one. However, this reveals lack of
knowledge in the field of exact influence of the
boundary conditions, during excavation process, to the
dynamic behavior of the machine.
The excitation band for the bucket wheel excavator
SchRs 4600.50 was established. Having no information
about the characteristics of the excitation signal it was
possible to estimate its general character on the basis of
the response of the structure.
ACKNOWLEDGMENT
Research co-financed by the European Union within the
European Social Fund.
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ПРОЦЕНА КОРЕЛАЦИЈЕ ИЗМЕДЈУ НУМЕРИЧКИХ
И ЕКСПЕРИМЕНТАЛНИХ ДИНАМИЧКИХ
КАРАКТЕРИСТИКА РОТОРНОГ БАГЕРА СА
АСПЕКТА РАДНИХ УСЛОВА
Eugeniusz Rusiński, Jerzy Czmochowski,
Przemysław Moczko, Damian Pietrusiak
Рад представља покушај аутора да изврше
валидацију нумеричког модела на основу резултата
експеримената. Модални критеријум квалитета
304 ▪ VOL. 41, No 4, 2013
измедју нумеричког и експерименталног модела је
изабран као меродавни фактор. Осим тога, поново
су размотрене промене фреквенција и степена
слободе који највише утичу на ниво корелације.
У већини случајева, нумерички и експериментални
модели не укључују утицај радног оптерећења на
динамичко понашање конструкције. Код новог
приступа који обухвата радне услове мора се поново
размотрити структура нумеричког модела, јер стари
приступ више није валидан. Модална анализа
извршена на основу радног оптерећења даје добре
резултате, али не приказује стварно стање
конструкције у радним условима. У том случају,
имамо два посебна система са различитим
динамичким
карактеристикама.
Одређивање
модалног модела коришћењем радне модалне
анализе пружа информације о објекту који ради а
који је и предмет нашег интересовања. .
FME Transactions